Let AB be the given straight line. Describe a square equal to the given rectangle (I. 14.), and make BC equal to the side of the square.

Upon AB describe the semicircle ADB.

From B as centre with BC as radius cut this semicircle in D. Join BD, AD, and make AE equal to AD.

Then the difference of the squares on AB, AE is equal to the square on BC, that is, the given rectangle.

Proof. The angle ADB is a right angle (III 3);

therefore square on AB

wherefore square on BC

=

squares on BD, AD (I. 47)

= squares on BC, AE;

=

difference of squares on AB, AE (Ax. 3.) Therefore AB is divided in the point E, so that the difference of the squares on AB, AE is equal to the given rectangle.

Q. E. F.

1. J. EDWARDS, Burton-on-Trent.-Find, in gallons, by Hutton's general rule, the volume of a cask, length 46'9 in., bung diameter 30'6 in., head diameter 26'1 in. Also find, in gallons, the wet ullage of a standing cask, length 30 in., bung diameter 27 in., head diameter 23 in., wet ullage 10 in. (Excise Exam., May, 1882.)

Dr. Hutton's general rule for finding the volume of a cask :Add into one sum 39 times the square of the bung diameter, 25 times the square of the head diameter, and 26 times the product of the two diameters; then multiply this sum by the length, and the product again by 000031 for the content in gallons. (The dimensions of the cask must be expressed in inches.)

Proof.--The angle ABF = the angle OBN, (Ax. 11.)
.. the angle NBF = the angle ABO; (Ax. 3.)

wherefore in the triangles BNF, AOB,

the angles BNF, NBF=the angles AOB, ABO, each by each, and the side BF the side AB,

... therefore the triangles are equal in all respects; (I. 26.) wherefore FN=AO, and BN = BO,

also triangle BNF = triangle AOB.

Similarly it can be proved that KM-AO, CM=CO, and triangle CMK = triangle AOC.

Again, triangle BNF = triangle AOB,

and triangle CMK = triangle AOC,

.. triangles BNF, CMK together = triangle ABC.

(Ax. 2.)

Q. E. D.

2. PICKWICK.-Find the side of a square inscribed in a semicircle, whose radius is 5 feet.

C

VOL. II. No. 12,

School Surgery.

BY ALFRED CARPENTER, M.D. (LOND.), C.S.S. (CAMB.),
Vice-President of the British Medical Association.
XII.

DISLOCATIONS.

DISLOCATIONS are terms which are applied to displacements of the bones which go to form a joint when the natural position of a bone to its fellow is altered, and the joint between them rendered useless. They may be simple, as when there is no other damage than a more or less severe rupture of the surrounding ligaments (as the bands which connect them together are called), or they may be associated with fracture of some of the bony structures which enter into the formation of the joint.

A dislocation is said to be complete when the end of the bone is altogether separated from its fellow which made up the joint. It is incomplete when it is a partial dislocation only. Dislocations are of very frequent occurrence amongst schoolboys. They are generally caused by sudden falls or severe blows, so that the force of a muscle or the direction of the blow is suddenly brought to bear upon the head of the bone, deflecting it in a direction in which there is not sufficient strength in the envelopes to resist the force. The head of the bone is in consequence forced out of its socket or resting-place. They are simple when there is no injury inflicted upon the surrounding skin or muscles. They are compound when the integuments are torn, and there is blood effused externally through an open wound. They may be associated with fracture, the bone itself being broken either in its shaft or immediately into the joint: these latter, when compound-that is, when the interior of the joint communicates with the external air-are always of most serious consequence.

There are some general symptoms which belong to all dislocations, such as pain more or less severe, according to the extent of the luxation, the injury to the soft parts, and the sensitiveness of the patient. The limb cannot be moved, or if it is moveable it is very painful to move it. There is a depression in one place and an unusual lump in another. The position of the limb is different to that which is natural

VOL. II.

PRICE 6D.

POST FREE, 7 D.

to it when at rest. It should always be remembered that dislocations are more common among children as a result of a particular fall or injury. A similar fall or injury is more likely to be accompanied by fracture in old people. This arises from the fact that the bones are more brittle in age than in youth. They have more of the lime salts and fatty matter in their composition, with less gelatine, whilst the opposite holds among the young. Dislocations occur most frequently in the following order :-The Shoulder; the Wrist, Fingers, and Thumb; the Ankle; the Elbow; the Collar-bone; the Hip; the Knee and Knee-cap; the Jaw. There are some minor forms which are very infrequent, and some more serious, as when a vertebra, or one of the bones of the neck or back, is displaced. In the latter case it is usually accompanied by immediate. death, and need not be considered here. The treatment in all kinds of dislocation is more or less similar in some of their parts, so that a few general directions may be given. The cardinal line is that all dislocations should be reduced as quickly as possible. A luxation which has existed five minutes only is a trifle compared with a similar case in which the dislocation has been unreduced for twelve hours. Every hour during which the bone remains out of place increases the mischief; inflammation arises, and with it a tendency to spasm, and to tension in the surrounding muscles. Reduce the dislocation if possible before the patient recovers from the shock of the accident; it is an easy thing to do if done at once; it becomes very serious if it be left for some time unreduced. reduction may be effected by any one if it is recognised immediately and the right course adopted: but if left until to-morrow, it is only the surgeon who will be likely to recognise it or able to reduce it.

The

Dislocation of the Shoulder.-This may take place in three different directions. The head of the bone may be thrust forward upon the chest, or backward on the shoulder-blade, or downwards into the arm-pit. The elbow cannot be brought close to the side without very severe pain. There is a cavity where the roundness of the shoulder should be, and the outline is too square. If the head of the bone is forward, it will be felt as a lump on the front of the ribs; or, if backward, upon the shoulder-blade, the head is felt as a ball upon the bone, or it may have disappeared into the armpit. This latter is the most painful form, for the head of 2 Q

the bone is pressing upon the nerves and blood-vessels which supply the limb. These dislocations are easily distinguished in the thin boy, but not always so in the muscular or fat boy. If the dislocation is recognised at once, any one may easily reduce it by placing the patient in the recumbent position on the ground, then pulling off his boot, sitting by the side of the patient on the side which is injured, and placing the foot in the arm-pit, and forcibly pulling at the elbow downwards with both hands towards the feet of the patient. The head of the bone will go into its socket with a snap, and the patient will be comparatively comfortable at once. If this is effected immediately after the accident, there is no occasion for the jack-towel or other ligatures which are suggested in some popular manuals. The operator's foot in the arm-pit and a strong grasp of the injured arm at the elbow, with traction firmly and continuously applied, will reduce the dislocation in a very short time, unless the head of the bone or the socket of the shoulder-blade are broken. In such cases the attendance of the surgeon must be sought before the reduction will be effected; but this kind of fracture, though common to old people, is unusual to children. As soon as the reduction is effected, the arm should be put into a sling, which may consist of a silk handkerchief hung round the neck, only just supporting the fore-arm and wrist, and keep ing the arm closely to the side. It is not necessary to place a pad in the arm-pit, and bandages are not required, provided the arm is not raised.

Dislocation of the Wrist and Fingers.-The wrist may be dislocated either forward or backward. It is seen at once by the position of the hand. Grasp the hand firmly, and let an assistant take the arm at the elbow and each pull gently but steadily in opposite directions. The limb resumes its natural shape. It should then be placed upon a pillow, the patient sitting at a table until a proper cradle is prepared for it. This may consist of an old book-cover, a piece of pasteboard, or bit of the leather of an old saddle (pig's skin), or a piece of gutta-percha. It should be put in hot water so as to completely soften it, then cover it with cotton wadding, and placing the injured limb upon it, mould it to the arm from the elbow to the knuckles, turning it round the outer side so as to form a kind of spout, in which it may rest when the limb is placed in a sling; bind it loosely on with a linen bandage, and allow it to dry without changing the position of the arm. It must not be put on too tightly, or it will have to be removed on account of the natural swelling which will take place. The same course should be taken with individual fingers; but in that case it is not necessary to do more than envelope the finger and its neighbour, leaving the wrist free. There may be much difficulty in reducing dislocation of the thumb, unless it is done immediately. A surgeon will have to be summoned and chloroform probably administered before a satisfactory reduction can be effected. Dislocation of the ankle is somewhat similar to that of the wrist, but it is usually something more. There are three bones contained in its formation. It is a common thing for the bones at the wrist to be broken in old people and to simulate dislocation; the rule will generally be fracture at the wrist in the aged, but dislocation in children from a similar accident; but dislocation at the ankle always has more or less of fracture in it, and should be treated, if possible, by a surgeon from the first. There may be

displacement in four directions, backwards, forwards, inward, or outward. The lateral dislocations will be self-evident, but the anterior or posterior are more difficult to distinguish, the heel being more prominent than usual, or less so, with great pain on the least movement being attempted. These symptoms will be sufficient to excite suspicion as to its nature, and should lead the principal to seek for surgical aid at once.

Dislocation of the Elbow.-Three bones enter into the formation of this joint, and like the ankle it may be dislocated in four directions, and will require skilled aid to effect its reduction, as it is often associated with fracture, and is a very serious injury.

Dislocation of the Collar Bone can scarcely be treated without skilled surgical assistance. There may be dislocation either at the shoulder or at the internal extremity of the bone where it rests upon the breastbone. In either case it will be requisite to follow the directions of a skilful surgeon as to bandages and position, although if reduced by pulling the shoulder outwards immediately, it may slip into its place and remain there, provided the arm and shoulder are fixed in that position and are not moved again for some time, a pad being placed in the armpit, and the arm bandaged to the sides.

A

Dislocation of the Hip is a very serious injury, but if recognised quickly it may be reduced by a non-surgical hand, and the patient saved much suffering. trifling injury sometimes seems to produce the deformity which results from it. The limb is shortened, the knee stands forward, and the toes rest upon the instep of the other foot. It is manifest when the patient stands erect. A jack-towel or some similar article should be passed between the thighs, and fastened securely above the head to something which will give fair purchase; another towel is passed round the thigh above the knee, and secured with clove hitch or sailor's knot, and the other end of the second towel being placed round the shoulders of the surgeon, he places his heel in the groin, and grasping the limb, guides it as he makes extension until it goes into its socket with an audible snap. Every minute which elapses after the injury before reduction is effected adds materially to the pain to the patient and trouble in effecting reduction.

Dislocation of the Knee.-This accident takes place in different directions, and considerable force is required to overcome it, which must be directed by a skilled hand. It is not a very common occurrence, but dislocation of the knee-cap is not uncommon. The little bone which lies in front of the knee-joint may be dislocated to the right or left, and when recognised immediately may be easily reduced by pressing suddenly upon the edge of the bone to the outer side of the joint, so as to press down the outer side, and at the same time tilt up the inner edge, and when the muscles attached to its upper border will bring it into position. If this does not effect the purpose aimed at, the leg of the patient, who is to lie on his back, must be bent as far as possible towards the face, when the leg should be suddenly bent back upon the thigh till the heel comes near to the hip. The operator presses the rim of the bone as he quickly straightens the leg again.

All dislocations require rest; warm applications to soothen the joint; no tight bandages should ever be used, but only those appliances which give gentle support.

his

Dislocation of the Jaw is very alarming, but soon remedied if it is recognised at once. The victim finds himself in a moment after gaping, or a blow, with the mouth wide open and incapable of speech. He can only indicate its nature by signs. The operator seats the patient in a low chair, and wrapping some leather or other tough material around thumbs, stands before the patient, and placing the thumbs as far back as possible on the back of the lower jaw, he depresses the jaw by pressing upon the back teeth; at the same time presses the jaw forward with the fingers under the chin. If the thumbs are not fully protected they will be severely bitten as the jaw closes, but the deformity is at once remedied. It is very likely to recur in those who have been once subject to it. The use of chloroform enables a skilled hand to reduce some kinds of dislocations much more satisfactorily than used to be the case; but its use for such a purpose can only be made by a surgeon.

Fractures, or Broken Bones.-There are some general directions regarding fractions which should be known to all persons having the care of children.

It would be a great advantage if ambulance classes were made a part of the work of school life, so that children might be taught some of those commonsense rules which, if always carried out, would diminish the incidence of misfortune by reducing it to its first consequences. It is very usual if a person steps off a curb, or falls downstairs, or from a tree, for the bystanders to endeavour to put him on his legs again. They take hold of him anywhere, perhaps by the arm, which may be broken; or lift him up by the shoulders, when, if his thigh be damaged, they complete the fracture, which may have been only partial; or they try to make him stand, and a splinter from a broken bone in the leg at once pierces through the skin, and makes a simple fracture into a compound one. By this means a comparatively trivial accident becomes a very dangerous one, and limb or life may be lost by the injudicious action of ignorant friends in thus trying to help an injured person to stand up. The first thing to be done when an accident happens is to keep the patient in the recumbent position until the nature of his injury is manifest; advise him to be still, and to indicate the part which is damaged. Limbs may be straightened by extending them, but in no case should any course be taken which may lead to shortening, and care should always be taken to prevent the completion of a fracture. A so-called green-wood fracture is easily kept in position. It is like a piece of green wood, it is still in apposition in some of its parts, and can only require lateral support to keep it in proper position, and will not shorten. When it is the leg or the thigh which is damaged, this rule is especially necessary to be observed: do as is generally done with horses when they fall upon a city pavement; keep the head down, until arrangements have been made for his safe transport by stretcher to his home. He must be raised very carefully to get the stretcher underneath him. First roll him on one side, and place one edge of the stretcher beneath him, and then roll him back very gently; or, if it be the thigh which is broken, lift him by the shoulders and the knees, keeping the latter close together, the legs bent upon the thighs, and with a roll of clothes beneath them, so that legs hook over the roll, and prevent shortening as much as possible. If it be the leg which is broken the limb should be placed upon a

pillow or some other soft material, raised a few inches by it, and the foot secured so as not to allow it to roll to the right or to the left. A soft pillow is the best adjunct; when it cannot be obtained, some hay or green grass arranged as a bed will effect the object aimed at.

Fractures are 1. Simple; 2. Compound; 3. Comminuted. They are simple when there is no outward damage to skin; compound when the bone pierces through the outer skin; and comminuted when the bone is broken into several pieces. It is very important to keep the malpositions which attend a fracture within the smallest possible compass, to prevent shortening, and on no account put on any kind of bandages too tightly. A bone is generally known to be broken by the grating feeling which arises from the broken ends rubbing together, and which are quite different to any other feeling which can be conveyed to the hand of the operator. This sound is called a crepitus, and is quite distinctive. A broken bone should be straightened by extending the lower end until the original shape of the limb is restored. It should be secured upon or within a pillow in the case of the leg, or with soft pads in the case of the arm, until a surgeon can take charge of it. In compound fracture it is best to cover up the wound as quickly as possible with carbolised oil, so as to keep it from contact with the external air; to wrap it up in its own blood, and prevent, as far as possible, the movement of the limb until it has been properly secured.

In Fracture of the Ribs the treatment consists in passing a flannel bandage round the chest, so as to limit the movement of the ribs, and compel the diaphragm (that is, the muscle between the chest and the abdomen) to do most of the work of respiration. The accident is recognised by the sharp pain on inspiration, giving rise to difficulty of breathing immediately after a fall or blow.

In Fracture of the Thigh-a misfortune which may happen to children with brittle bones-the patient should be kept on his back, with a bolster or some similar firm support under both knees, which should be secured together until the surgeon has arranged a proper bed. Compound comminuted fractures must be treated by the surgeon as soon as possible.

In closing the second series of instructions to teachers on medical subjects, it will be manifest that it is necessarily superficial in many parts, it being only possible to indicate the nature of an injury, without further instructions. Some of the deficiencies on strictly medical points will be remedied in the subsequent numbers of the PRACTICAL TEACHER, under the head of 'The Teacher's Health.'